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JEECONCEPTSBOOSTER
APPLICATIONOFDERIVATIVES
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
1.DERIVATIVEASARATEMEASURE
1.Introduction:averagerateandinstantaneousrate
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
1.DERIVATIVEASARATEMEASURE
2.Rateofchangeingeometry
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
1.DERIVATIVEASARATEMEASURE
3.Rateofchangeinmotion
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
1.DERIVATIVEASARATEMEASURE
44.Rateofchangeincostandrevenue
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
2.INTERPRETATIONOFDY/DXASARATEMEASURE
1.Ratewhendimensionsareincreasingordecreasing
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
2.INTERPRETATIONOFDY/DXASARATEMEASURE
2.Sunlightpoleheightproblem
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
2.INTERPRETATIONOFDY/DXASARATEMEASURE
3.kiteproblemstickonwallinsleeping
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
2.INTERPRETATIONOFDY/DXASARATEMEASURE
4.ProblemofWaterflow
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
93.APPROXIMATIONS
1.Differentialsdefinitions(intermsofsmallchange)andexamples
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
3.APPROXIMATIONS
2. Absolute error; relative error and percentage error and Geometric meaning ofdifferentialsandalgorithm
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
3.APPROXIMATIONS
3.Timeperiodofpendulumproblem
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
3.APPROXIMATIONS
4.Calculationofapproximatevalue
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
3.APPROXIMATIONS
5.Calculationofsquarerootandcuberoot
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
3.APPROXIMATIONS
6.Findtheleastvalueofkforwhichthefunctionx2 + kx + 1isanincreasingfunctionintheinterval1 < x < 2
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
1.Rolletheorem:statementordefinition
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
2.Geometricmeaningofrollestheoremanditsuse
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
3.Applicabilityofrollestheorem
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
4.VerifyRollTheorem
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
5.DeterminesolutionofequationusingRolleTheorem
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
6.LMVT:Statement;proofandGeometricalinterpretation
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
7.VerificationofLMVT
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
4.MEANVALUETHEOREMS
8.ProveinequalitiesusingLMVT
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
234.MEANVALUETHEOREMS
9.Cauchysmeanvaluetheorem
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
5.EQUATIONOFTANGENTSANDNORMALS
1.Slopeoftangentandnormal
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
5.EQUATIONOFTANGENTSANDNORMALS
2.Equationofnormalandtangents
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
5.EQUATIONOFTANGENTSANDNORMALS
3.Findingtheequationsoftangentandnormaltoacurveatapoint
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
5.EQUATIONOFTANGENTSANDNORMALS
4.Lengthoftangent;normal;subtangentandsubnormal
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
5.EQUATIONOFTANGENTSANDNORMALS
5.Findingtheequationsoftangentandnormalparallelorperpendiculartoagivenline
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
5.EQUATIONOFTANGENTSANDNORMALS
6.Findingtheequationofthecurve
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
6.ANGLEBETWEENTHECURVES
1.Anglebetweentwocurves:howitisequaltoanglebetweentangents
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
6.ANGLEBETWEENTHECURVES
2.Showthatthecurvesx = y2andxy = kcutatrightangles;if8k2 = 1
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
7.MISCELLANEOUSAPPLICATION
1. Find the possible values of p such that the equation px2 = lnx has exactly onesolution.
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
1.Whatisincreasingordecreasingfunction
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
2. Find the locus of point on the curve y2 = 4a x + asinxa
where tangents are
paralleltotheaxisofx
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
3.Solve:4x3 - 24x2 + 44x - 24 > 0
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( ( ))
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
4.Strictlyincreasingfunctionsandstrictlydecreasingfunctions
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
5.Showthatthefunctionf(x) = x2 isneitherstrictly increasingnorstrictlydecreasingonR.
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
6.Letfbecontinuouson[a; b]anddifferentiableon(a; b)Iff(x)isstrictlyincreasingon(a; b) then f′ (x) > 0 for all x ∈ (a; b) and if f(x) is strictly decreasing on (a; b) thenf′ (x) < 0forallx ∈ (a; b)
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
7.Letfbeadifferentiablerealfunctiondefinedon(a; b)andiff′ (x) > 0forallx ∈ (a; b)thenfisincreasingon(a; b)andiff′ (x) < 0forallx ∈ (a; b)thenf(x)isdecreasingon(a; b)
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
8.MONOTONOCITY
8.Findtheintervalsinwhichf(x) =xlogx
isincreasingordecreasing
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
9.MAXIMAANDMINIMA
1.Maximumandminimumvalueoffunctioninitsdomain
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
9.MAXIMAANDMINIMA
2.Findmaximumandminimumvalue;ifany;forf(x)=-|x-1|+5forallxinR
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
10.TESTSFORLOCALMAXIMUM/MINIMUM
1.Localmaximumandlocalminimumandconditionforit
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
10.TESTSFORLOCALMAXIMUM/MINIMUM
2.Conditionofextremum
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
10.TESTSFORLOCALMAXIMUM/MINIMUM
3.Firstderivativetestforlocalmaximaandminima(methodandhowitcomes)
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
10.TESTSFORLOCALMAXIMUM/MINIMUM
4.Higherorderderivativetest
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
10.TESTSFORLOCALMAXIMUM/MINIMUM
5.Findallthepointsoflocalmaximaandminimaofthef(x)=x^3-6x^2+9x-8
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
11.TESTSFORGLOBALMAXIMUM/MINIMUM
1.GlobalMaximumandMinimumandtherequiredcondition
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
12.POINTOFINFLECTION
1.Pointofinflectionandpointofinflexion
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
13.PROPERTIESOFMAXIMAANDMINIMA
1.Propertiesofmaximaandminima
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
14.APPLICATIONOFEXTREMUM
1.Maximaandminimaincloseinterval
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
14.APPLICATIONOFEXTREMUM
2.ApplicationsofMaximaandminimainGeometry
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
14.APPLICATIONOFEXTREMUM
3.ApplicationsofMaximaandminimainalgebra
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
14.APPLICATIONOFEXTREMUM
4.ApplicationsofMaximaandminimaintrigonometry
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
14.APPLICATIONOFEXTREMUM
5. Find two positive numbers whose sum is 14 and the sum of whose squares isminimum
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CONCEPTFORJEE||ChapterAPPLICATIONOFDERIVATIVES
14.APPLICATIONOFEXTREMUM
6.Findthepointonthecurvey^2=4xwhichisnearesttothepoint(2;-8)
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